In this document, I will use the word “light” interchangeably with “optical radiation,” understanding that a range of invisible wavelengths which propagate similarly to light are included when either term is used.
The most common techniques for generating coherent light involve laser action. Laser action occurs when atoms or molecules in their excited state generate and amplify light at a specific wavelength determined by the energy difference between the excited state and the unexcited state of the atom or molecule. There is a limited set of wavelengths at which coherent light can be efficiently, reliably, and economically generated using direct laser action. Laser oscillators make use of laser gain and feedback to generate coherent light, and as a general rule do not need coherent light as an input.
A set of techniques known collectively as “nonlinear optics” make use of “optical mixing” to generate coherent light, using coherent light as an input. The light generated by optical mixing may be at a different wavelength from the input, or at the same wavelength but with amplified power. This expands the set of wavelengths at which coherent light can be generated and amplified beyond the set provided by laser action by itself. A widely used type of optical mixing is second harmonic generation, also known as frequency doubling, in which coherent light is generated at an optical frequency twice the optical frequency of the input. The wavelength of the output light produced by second harmonic generation is one-half the wavelength of the input light. This can be understood by considering the relationship between optical frequency and wavelength, which states that the product of the optical frequency and the wavelength is the invariant speed of light, according to the equationc=λv   (Eq. 1)where c is the speed of light, λ is the wavelength, and v is the optical frequency.
In this document I will sometimes specify light by its wavelength, and sometimes by its optical frequency. Since the product of these two is the invariant speed of light, the specification of one specifies the other, and vice versa.
A type of optical mixing closely related to second harmonic generation is known as sum frequency generation. In sum frequency generation, the optical frequency of the generated light is at the sum of the optical frequencies of the two inputs, according to the equationv3=v1+v2   (Eq. 2)where v3 is the newly generated output optical frequency, and v1 and v2 are the two input optical frequencies. Second harmonic generation can be seen to be a special case of sum frequency generation, for the case of the two inputs being the same, that is to say, for the case of v1=v2.
An equation relating the wavelength of light generated by sum frequency generation to the wavelengths of the inputs, derived by combining Eqs. 1 and 2, is:1/λ3=1/λ1+1/λ2   (Eq. 3)where λ3 is the newly generated output wavelength, and λ1 and λ2 are the two input wavelengths.
Another type of optical mixing is difference frequency generation, in which the generated light is at an optical frequency which is the difference between the optical frequencies of the two inputs. Equation 4 relates the optical frequencies involved in optical difference frequency generation, and is similar to Eq. 2, except that now v2 must be the larger of the two input optical frequencies, and v1 must be the smaller of the two input optical frequencies. The difference frequency, v3, is the newly generated output frequency.v3=v2−v1   (Eq. 4)
By combining and then simplifying Eq. 1 and Eq. 4, it can be shown that the wavelengths involved in difference frequency generation are related by the equation1/λ3=1/λ2−1/λ1   (Eq. 5)where λ2 is the shorter of the two input wavelengths, λ1 is the longer input wavelength, and λ3 is the newly generated wavelength.
There is a distinction between sum frequency generation and difference frequency generation relating to which optical frequencies grow in power, and which get depleted. In sum frequency generation, the coherent light at the newly generated optical frequency v3 increases in power at the expense of both of the two inputs, at optical frequencies v1 and v2. However, for difference frequency generation, the light at the lower input frequency v1 as well as the newly generated frequency v3 increase in power, at the expense of the light at the higher input frequency v2. Thus difference frequency generation can be used both to generate a new frequency v3, found by subtracting the lower from the higher of the two input frequencies, and to amplify light at the lower input frequency v1, all at the expense of the light at the higher input frequency v2. Amplification is a form of generation, for the case where the newly generated light is at a wavelength that is already present. This process of amplification, which is inherent in difference frequency generation, is often called “optical parametric amplification.” The distinction between difference frequency generation and optical parametric amplification is simply in which output beam is utilized.
Optical mixing can in principle take place in any material, but sum and difference frequency generation take place efficiently only in crystals. Thus the material in which optical mixing occurs will be referred to as a nonlinear crystal.
A good reference on these general facts of optical mixing is “Nonlinear Optics”, Third Edition, by Robert W. Boyd, published by Academic Press in 2008.
A useful feature of optical mixing is that when light at one input optical frequency v1 is modulated, and the light at the other input optical frequency v2 is not modulated, then the output light at optical frequency v3 after optical mixing will have exactly the modulation of the light at the first optical frequency v1 (except for a possible change of sign.) Thus not only power can be transferred between different optical frequencies, but also modulation. The two types of modulation are phase modulation and amplitude modulation, and both are transferred from the input optical frequency to the generated optical frequency.
To say that light is not modulated is equivalent to saying that the light consists of a single optical frequency, rather than the range of optical frequencies present in all natural light and most laser light. Optical mixing with one of the inputs consisting of a single optical frequency will result in the modulation of the other input being transferred to the newly generated output. I will use the expression “single-frequency oscillation” to describe laser oscillation which produces light which for practical purposes consists of a single optical frequency. A “single-frequency laser” is a laser oscillator which produces light which for practical purposes consists of a single optical frequency.
In the simplest configuration for optical mixing, two beams of light to be optically mixed pass through a nonlinear crystal, with no feedback path in either beam. Such designs tend to be inefficient for beams of low and moderate powers, with only a small fraction of the light converted to the new optical frequency. An important feature of optical mixing is that the efficiency of the process increases with the input power, until efficiency is limited as it approaches the ideal efficiency of 100%. Thus, only at relatively high power is the optical mixing process efficient. For the robust and reliable nonlinear material lithium triborate (chemical formula LiB3O5, common name LBO), input power in excess of 1000 watts is needed to reach a good level of efficiency, such as 50% conversion. Even for less-robust nonlinear materials such as periodically poled lithium niobate (LiNbO3), which suffers from degradation when used in the visible or ultraviolet, a power of greater than 10 watts is needed in order to reach 50% efficiency.
A prior-art technique for improving efficiency is described by Dixon et. al. in U.S. Pat. No. 4,879,723, issued in 1989. In Dixon's design, the nonlinear crystal is placed inside the resonator of a laser, so that it is traversed by the internal resonant beam of the laser. One of the beams of light to be optically mixed (by sum frequency generation, in this case) is the internally circulating beam within the laser resonator. The other comes from an external source, specifically for Dixon's design, from a laser diode. This approach has two advantages. First, the internally circulating beam within the resonator has a higher power, due to the feedback within the resonator, and this higher power improves the efficiency of the optical mixing process. Second, for the beam which is resonant, light not converted in one pass through the nonlinear crystal is recycled due to the feedback of the resonator, and has additional opportunities to be converted, again raising efficiency.
For the level of power typically available from practical lasers, Dixon's design will still have low efficiency, especially when robust nonlinear materials such as LBO are used. Concentrating the laser energy into pulses would improve efficiency, since the instantaneous power can thereby be much higher than the average power, and instantaneous power is what determines the conversion efficiency of optical mixing. Roughly speaking, considering an optical mixing process with a fixed level of average power available, the efficiency can be doubled by concentrating the light into pulses with a peak instantaneous power twice the average power. With peak power ten times the average power, efficiency is increased tenfold. Of course, these efficiencies are ultimately limited as efficiency approaches 100%, but this simple rule gives a rough guide to the large enhancement to efficiency that is possible by pulsing the light to be converted.
Often, a pulsed beam is what is desired for an application, as is the case for laser radar and materials processing.
Thus both for efficiency and utility, pulsed light is desired in place of the steady, or continuous-wave, light described by Dixon.
A prior-art technique for optical parametric amplification is described by Gunnar Arisholm, Ørnulf Nordseth, and Gunnar Rustad, “Optical parametric master oscillator and power amplifier for efficient conversion of high-energy pulses with high beam quality,” Optics Express, vol. 12, no. 18 (6 Sep. 2004). Though this paper describes successful efforts to achieve improved beam quality, the beam quality is “high” only in comparison with earlier optical parametric amplifiers. The beam quality parameter they achieved was M2=2.3, where a value of M2=1 is perfect, and typical lasers used for laser radar must have M2 less than 1.3. When beams are generated by optical mixing at low efficiency, the beam quality of the output is typically as good as the beam quality of the input. When conversion efficiency gets higher, it becomes difficult to generate a beam which has good beam quality. This is due to the complex effects which take place as the input beam is significantly converted, or “depleted.” Once a beam is fully depleted, back-conversion occurs—which means that the generated light is “back-converted” to the input wavelength! For a realistic beam, which is more intense on center than off-center, 100% conversion occurs on-center before the efficiency over the whole beam reaches 50%. But if you increase total beam power to improve efficiency off-center, the center back-converts, actually dropping in efficiency, and you get a beam with a dip in the center.
It would be desirable to break the connection between depletion and efficiency, and to create a design which is efficient but has low depletion, so that beam quality could be maintained.
Denman et. al., in U.S. Pat. No. 7,035,297 issued in 2006, disclosed a design for a sum-frequency generator based on resonating both of the frequencies to be summed in the same resonator, which is an external resonator instead of a laser resonator. This design is efficient, but it requires that both of the input beams be unmodulated, single-optical-frequency light. This eliminates the possibility of transferring modulation on the input beam to the output beam. Also, it requires precise matching of the light into the external resonator, creating difficult tolerances on both alignment and cavity length. Though the Denman design has been successfully used to excite mesospheric sodium atoms, as needed to produce artificial guide stars for astronomy, the lack of modulation reduces the efficiency of sodium excitation, and the challenging tolerances make the design expensive to produce.
It would be desirable to have a device which can efficiently convert pulsed, modulated light at one optical frequency to another optical frequency, while maintaining the modulation.